estimate_risk: Calculate information criteria.

Description

This function uses the degrees of freedom to calculate various information criteria. This function uses the "unknown variance" version of the likelihood. Only implemented for Gaussian regression. The constant is ignored (as in stats::extractAIC()).

Usage

estimate_risk(object, x, type = c("AIC", "BIC", "GCV"), approx_df = FALSE)

Value

a data.frame with as many rows as object$lambda. It contains columns lambda, df, and the requested risk types.

Arguments

object: fitted object from a call to sparsegl().
x: Matrix. The matrix of predictors used to estimate the sparsegl object. May be missing if approx_df = TRUE.
type: one or more of AIC, BIC, or GCV.
approx_df: the df component of a sparsegl object is an approximation (albeit a fairly accurate one) to the actual degrees-of-freedom. However, the exact value requires inverting a portion of X'X. So this computation may take some time (the default computes the exact df).

References

Liang, X., Cohen, A., Sólon Heinsfeld, A., Pestilli, F., and McDonald, D.J. 2024. sparsegl: An R Package for Estimating Sparse Group Lasso. Journal of Statistical Software, Vol. 110(6): 1–23. tools:::Rd_expr_doi("10.18637/jss.v110.i06").

Vaiter S, Deledalle C, Peyré G, Fadili J, Dossal C. (2012). The Degrees of Freedom of the Group Lasso for a General Design. https://arxiv.org/abs/1212.6478.

Examples

Run this code

n <- 100
p <- 20
X <- matrix(rnorm(n * p), nrow = n)
eps <- rnorm(n)
beta_star <- c(rep(5, 5), c(5, -5, 2, 0, 0), rep(-5, 5), rep(0, (p - 15)))
y <- X %*% beta_star + eps
groups <- rep(1:(p / 5), each = 5)
fit1 <- sparsegl(X, y, group = groups)
estimate_risk(fit1, type = "AIC", approx_df = TRUE)